General approach to waveform inversion

The above section presented the approach to frequency-domain waveform inversion used in this study. The general computational flow is described the pseudo-code in figure 1.

 

flowchart Figure 1 Flow chart describing the processing flow for waveform inversion.

The procedure begins with the forward wavefield modeling (equation 1) for the first non-linear iteration at the first frequency. Wavefield residuals are then computed (equation 2) and back-projected throughout the model volume (the adjoint of equation 1), enabling the computation of the single-source gradient vector (equation 9). This procedure is repeated for all shot points until the total gradient field is computed by stacking single-source gradient profiles. The conjugate gradient direction is then calculated from the current and past gradient vectors (equation 11), and the step length is computed by summing the forward modeling results of the linear perturbation Frech${\'e}$t matrix (equation 12). This process is repeated for the desired number of iterations, or until convergence is reached. The entire process is then repeated at the next highest frequency until inversion of all chosen frequencies is complete.